# Exercises

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1. For the following sets of data, find to one decimal place
1.
1. the mean
2. the median, and
3. the mode
2. For the following sets of data, find
1.
1. the mean
2. the median
3. the mode
Briefly describe the positions of the mean, median and mode and their relation to one another for each data set.
1.
Table 1
x frequency
-2 3
-1 7
0 8
1 5
2 4
2.
Table 2
x frequency
6.3 2
6.4 1
6.5 6
6.6 5
6.7 13
6.8 4
3.
Table 3
x frequency
1 15
2 5
3 3
4 1
5 2
3. For each of the following stem and leaf plots, find
1. the median, and
2. the modal-class interval
1.
Table 4
Stem Leaf
2 2 3 8
3 1 1 4 2
4 2 2 3 5 8 9 9
5 2 4 7 7 8
6 0 3 2
7 4
Stem 4, Leaf 2 represents 42 Answer 3a
2.
Table 5
Stem Leaf
0(0) 2
0(5) 5 6 8
1(0) 0
1(5) 5 5 6 6 7 8 8 9
2(0) 0 0 0 1 1 2 3 3 3 4 4 4
2(6) 6 6 7 8 8 9 9
3(0) 0 4
3(5) 5 6 7 7 8
Stem 3, Leaf 5 represents 35 Answer 3b
4. Imagine that the annual population increases over a 10 year period are given in the table below:

Table 6. Population increase
Year Increase from previous
1 53,377
2 52,170
3 67,000
4 90,332
5 72,681
6 65,226
7 76,777
8 83,657
9 77,753
10 82,892
5. Forty students took a math test marked out of 10 points. Their results were as follows:

9, 10, 7, 8, 9, 6, 5, 9, 4, 7, 1, 7, 2, 7, 8, 5, 4, 3, 10, 7,
3, 7, 8, 6, 9, 7, 4, 2, 3, 9, 4, 3, 7, 5, 5, 2, 7, 9, 7, 1

1. Prepare a frequency table of the scores. Answer 5a
2. Using the frequency table, calculate the mean, median and mode. Answer 5b
3. Interpret these results. Answer 5c
6. Imagine that the number of unemployed people is given in the table below

Table 7.  Unemployment
Age group No. unemployed
15 to 19 3,688
20 to 24 4,031
25 to 34 5,432
35 to 44 4,360
45 to 54 3,162
55 to 64 1,702
7. A random survey of 100 married men gave the following distribution of hours spent per week doing unpaid household work:

Table 8.  Hours spent per week doing unpaid household work
Hours No. of men
0 to < 5 1
5 to < 10 18
10 to < 15 24
15 to < 20 25
20 to < 25 18
25 to < 30 12
30 to < 35 1
35 to < 40 1
8. The following is a hypothetical table of annual income of people aged 15 years or more:

Table 9.  Annual income of people aged 15 years or more
Income (\$) Persons
0 to 2,079 114,195
2,080 to 4,159 44,817
4,160 to 6,239 45,862
6,240 to 8,319 139,611
8,320 to 10,399 114,192
10,400 to 15,599 148,276
15,600 to 20,799 123,638
20,800 to 25,999 121,623
26,000 to 31,199 103,402
31,200 to 36,399 73,463
36,400 to 41,599 59,126
41,600 to 51,999 68,747
52,000 to 77,999 56,710

## Class activities

1. Measure the height of each student in your class to the nearest centimetre. Are there any outliers? Use an appropriate method to find the mean, median and mode. Compare all three measures. Which value gives the best measure of central tendency? Why? Which organizations or companies would find such statistics useful?
2. Find out what your grade or school's student population has been for the last 10 years. Are there any outliers? Use an appropriate method to find the mean, median and mode. Compare all three measures. Which value gives the best measure of central tendency? Why? How would your school or school board use such statistics?
3. Find the final scores of your favourite school sport from your school's records. Collect the scores, both wins and losses, for the last 10 years. (If the data are not available, use data for your favourite sporting team.)
• What was the mean final score, including both wins and losses, for the past 10 years?
• What was the median final score, including both wins and losses, for the past 10 years?
• Are any of the mean final scores similar to the corresponding median final score?
• Given these values, what can be said about the distributions?
• What are some of the problems you might come across in trying to use statistics to compare school or other sports teams of the past with those of today?
4. For ordinal data, can you think of occasions where the mode would be of more use than the median or mean? Discuss as a class.